In order to properly tune a piano according to the equally tempered scale, the notes are tuned such that the frequency ratio for each half step is constant at a value of 2.sup.1/12 which is equal to 1.059463. By standard and well established tuning procedure, the notes are tuned by listening to beats between an overtone of the note being tuned and an overtone of a selected note already tuned, and adjusting the string tension of the note being tuned to attain the intended beat rate. An exposition of standard piano tuning procedure is given in "Piano Servicing, Tuning and Rebuilding", Arthur A. Reblitz, Vestal Press, Vestal, N.Y., 1976, and "Piano Tuning, Repair and Rebuilding", Floyd A. Stevens, Nelson Hall Company, Chicago, Ill., 1972, reprinted 1977. This standard tuning procedure relies upon the practice and skill of the tuner in laying the temperament of at least one full octave, and then tuning the remainder of the keyboard in relation to the properly tempered octave. The intended beat note associated with the two struck notes is produced by overtones of the struck notes which are of lesser intensity than the fundamental tones and which may be masked by spurious beats and ambient noise. As a result, the desired beat note is often difficult to hear, especially without practice and skill.
Electronic tuning aids have been proposed heretofore, and have been based on a comparison of the pitch of a reference note provided by the tuning apparatus and that of a single note being tuned, and nulling of beats between the first harmonic (fundamental) of the notes being compared to thereby tune a note to the reference pitch. Examples of such tuning aids and described in U.S. Pat. Nos. 3,585,898; 3,766,818; 3,901,120 and 4,088,052. However, a piano cannot be tuned by pitch alone to achieve a musically satisfactory scale. A difficulty in tuning a piano by comparison of pitch between a note being tuned and a reference note is caused by the characteristic known as "stretch", caused by the finite, non-zero string diameter, and the stiffness of the strings, in which the overtones actually sounded by a piano string will occur at slightly higher frequencies than the mathematically specified harmonics. The effect of stretch tends to be greatest in spinet models which employ shorter string lengths than console or grand models. Thus, the harmonic frequencies specified for notes of a piano are somewhat idealized since in practice the scale must be stretched over its entire range in accordance with the characteristics of the particular piano. Since the desired frequencies of all of the keys are not known a priori, because of the stretch characteristics of the particular piano, the instrument cannot be readily tuned by pitch alone. The instrument can be recalibrated for each note tuned after the temperament of an octave is completed, but this procedure is very tedious. A technique is described in U.S. Pat. No. 3,968,719 in which a stretch correction is provided for the particular instrument, and the corrections then employed to calibrate a series of frequency tone generators and thereafter using the calibrated tone generators for adjustment of the pitch of the piano notes.